The problem of designing optimum receivers with a finite built-in delay, for a class of stochastic signals, is considered. The approach used here is based on the so-called fixed-lag smoothing techniques. Specific cases of amplitude and phase modulation are considered in detail to illustrate the type of optimal (suboptimal in the nonlinear case) receivers which are obtained using this approach. The performance of these finite-delay demodulators is compared with that obtainable using the ideal infinite-delay and the common zero-lag demodulators. It is found that introduction of a nominal delay results in a significant improvement in performance over the zero-lag demodulators, of course, at the cost of increased complexity.